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Simplifying 1.75n2 + -31.5n + -105 = 0 Reorder the terms: -105 + -31.5n + 1.75n2 = 0 Solving -105 + -31.5n + 1.75n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -60 + -18n + n2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -18n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + -18n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -18n + n2 = 0 + 60 -18n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 -18n + n2 = 60 The n term is -18n. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18n + 81 + n2 = 60 + 81 Reorder the terms: 81 + -18n + n2 = 60 + 81 Combine like terms: 60 + 81 = 141 81 + -18n + n2 = 141 Factor a perfect square on the left side: (n + -9)(n + -9) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (n + -9) equal to 11.874342087 and -11.874342087.Subproblem 1
n + -9 = 11.874342087 Simplifying n + -9 = 11.874342087 Reorder the terms: -9 + n = 11.874342087 Solving -9 + n = 11.874342087 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = 11.874342087 + 9 Combine like terms: -9 + 9 = 0 0 + n = 11.874342087 + 9 n = 11.874342087 + 9 Combine like terms: 11.874342087 + 9 = 20.874342087 n = 20.874342087 Simplifying n = 20.874342087Subproblem 2
n + -9 = -11.874342087 Simplifying n + -9 = -11.874342087 Reorder the terms: -9 + n = -11.874342087 Solving -9 + n = -11.874342087 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = -11.874342087 + 9 Combine like terms: -9 + 9 = 0 0 + n = -11.874342087 + 9 n = -11.874342087 + 9 Combine like terms: -11.874342087 + 9 = -2.874342087 n = -2.874342087 Simplifying n = -2.874342087Solution
The solution to the problem is based on the solutions from the subproblems. n = {20.874342087, -2.874342087}
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